The invention especially applies to the field of wireless communication systems for transmitting digital multi-carrier signals using, e.g., Orthogonal Code Division Multiplex (OCDM), Orthogonal Frequency Division Multiplex (OFDM), or High Speed Down Link Packet Access (HSDPA). In particular, the invention relates to systems and methods for linearizing power amplifiers with strong memory effects.
Conversion, modulation, and amplification are non-linear transformations, which can cause the violation of the spectrum emission requirements and/or a low operating efficiency. Linearization methods are used, therefore, in order to weaken this disadvantage. Predistortion is a linearization method which modifies the complex digital source signal x from the transmit path in such a way thatz=yxwherey>0is a real constant, and z is the complex digital amplifier output signal from the feedback path.
There are two different types of non-linearity: (a) Non-linearity in the common sense; it mainly causes the overall curvature which finally passes into the saturation shown in FIG. 4, light curve. (b) Non-linearity as a consequence of memory effects especially produced by the power amplifier; this non-linearity is indicated mainly by a noise-like shape of the AM-AM diagram in FIG. 4, dark curve. A predistortion method is searched for, which can handle both types of non-linearity.
A number of prior art predistorters are restricted to a predistortion based on multiplying the input sample x by a complex gain, see e.g. Linearization method for amplifier and amplifier arrangement, WO 99/57806, Transmitter Linearization, WO 00/36800, Amplifier Linearization by Adaptive Predistortion. U.S. Pat. No. 5,049,832, Kelly Mekechuk; Wan-Jong Kim; Shawn P. Stapleton; Jong Heon Kim: Linearizing Power Amplifiers Using Digital Predistortion, EDA Tools and Test Hardware. High Frequency Electronics, April 2004, p. 18-25, or Method for improving the output power of a non-linear power amplifier WO 2004/070943.
Letξ=x·Γ(|x|2)where x is a sample from the input signal to be amplified, ξ is a sample from the predistorted signal, and Γ is the complex gain. Γ is normally computed in comparing the digital complex input signal x with the digital complex power amplifier output signal z extracted from the feedback path. This approach is a good technique for handling non-linearities of type (a), however, it fails for non-linearities of type (b).
The complex gain approach can be extended toξ=x·Γ(|x|2,|x−1|2, . . . ,|x−k|2)with k≧1, where x is the present input sample, and wherex−i is the input sample i sample clocks before (1≦i≦k). The latter approach allows taking into account the “past” by considering previous samples; however, only the memory effect from the non-linearity (a) can be realized.
There are prior art predistorters e.g. disclosed in WO 2004/095715 or US 2005/0001684 A1 using an additive correction, e.g.ξ=x+C(|x|2)these predistortion types are quasi equivalent to those based on a complex gain.
Another type of adaptive predistorter uses a digital filter; see e.g. Method and apparatus for linear transmission by direct inverse modelling, WO 98/51047, where the filter coefficients are learnt in a similar manner as shown in FIG. 1. Filter approaches should have nearly the same performance than VOLTERRA-like approaches.
Volterra series is a general nonlinear power amplifier model; it has been successfully used to derive behavioural models for RF power amplifiers with memory effects, see e.g. Zhu, Anding & Brazil, Thomas J.: Adaptive Volterra-based Predistorter Design for RF High Power Amplifiers. IEEE 2001, 100-105. Mirri, Domenico et al.: A Modified Volterra Series Approach for Nonlinear Dynamic Systems Modelling. IEEE Transactions on Circuits and Systems—I. Fundamental Theory and Applications, 49, No. 8, August 2002, 1118-1128, or Raich, Raviv & Zhou, Tong G.: On the Modelling of Memory nonlinear effects of Power Amplifiers for Communication Applications. IEEE 2002, 7-10.
However, it has serious drawbacks: a large number of coefficients that must be extracted, and the exact inverse of a Volterra system is difficult to construct. The crucial point for such approaches is to find out an appropriate simplification of the VOLTERRA series and its inverse.
There are some suggestions for realizing predistortion with a simplified Volterra-like approach, see e.g. Chang, Sekchin & Powers, Edward: A Simplified Predistorted for Compensation of Nonlinear Distortion in OFDM Systems. IEEE 2001, 3080-3084 or Zhu, Anding & Brazil, Thomas J.: Adaptive Volterra-based Predistorter Design for RF High Power Amplifiers. IEEE 2001, 100-105, but performance seems to be insufficient for wideband CDMA signals. Thus, Zhu, Anding and Brazil, Thomas, Adaptive Volterra-Based Predistorter Design for RF High Power Amplifier, IEEE 2001, pp.100-105, presents simulation results only for an IS-95 CDMA signal.
Predistortion with the VOLTERRA system is usually realized by the complicated pth-order inverse technique, see e.g. Schetzen, M.: The Volterra and Wiener Theories of Nonlinear Systems. New York: Wiley, 1980, which turns out to be only an approximation. Amongst other things, two simplified cases of the Volterra model have been recently proposed to capture the memory effect: (i) A linear time-invariant (LTI) system followed by a memoryless nonlinearity (Clark, C. J. et al., Time Domain Envelope Measurement Technique with Application to Wideband Power Amplifer Modelling, IEEE Trans. Microwave Theory Tech. 46, 1998, pp. 2534-2540). Advantage of this so-called ‘Wiener modelling’: the corresponding predistorter is a Hammerstein system consisting of a memoryless nonlinearity followed by an LTI system, so that it is possible for the predistorter to be an exact inverse of the power amplifier model. (ii) A memory polynomial model according to
      ξ    n    =            ∑              j        =        1            J        ⁢                  ∑                  k          =          0                K            ⁢                        a          jk                ⁢                              x                          n              -              k                                ·                                                                  x                                  n                  -                  k                                                                                  j              -              1                                          
Similar to the Volterra model, an exact inverse of the memory polynomial is difficult to obtain; Ding et al. propose, therefore, another memory polynomial as an approximate inverse, see Ding, Lei; Zhou, G. Tong; Morgan, Denis R., Ma, Zhengxiang; Kenney, J. Stevenson; Kim, Jaehyeong; Giardina, Charles, R.: A Robust Baseband Predistorter Constructed using Memory Polynomials. IEEE Transactions on Communications 52, No. 1, 2004, 159-165. They argue that it is difficult to judge which power amplifier model is the best, since it could depend on the amplifier type, the data format being transmitted etc. Moreover, they argue that the most accurate power amplifier model may not be the most amenable to predistortion. They suggest, therefore, taking the linearization as the ultimate objective.
Adaptive digital predistortion: (i) Find a good model for the power amplifier model by unifying both, the latter approach with the memory polynomial approach. (ii) Learn this model by combining both aspects: to get the most accurate power amplifier characteristic, and to get the optimum linearization. (iii) Reduce the computational efforts by using a simple recursion formula for calculating the predistorted samples.